Senegal international Mane suffered a leg injury shortly before the World Cup in November but could feature on Sunday, coach Julian Nagelsmann told a news conference on Friday.
"Sadio will be in the squad. It's not enough yet for him to start. He has trained two and a half sessions with the team. So he will be in the squad which is an alternative that makes us very happy."
The Bavarians lost to Borussia Moenchengladbach last week and have managed just two wins in their six league games this year.
"Overall we have not achieved reached the results we would have wanted. We all know that we have to deliver," Nagelsmann said.
"At Bayern if you win all is quiet. If you don't it's not quiet. So we must win. This is a top match in the league and we know that the top spot is at stake."
Union will be buoyed by their stunning 3-1 victory over Ajax Amsterdam on Thursday to advance to the Europa League Round of 16 on their biggest European night.
"You cannot afford too many mistakes against them," said Nagelsmann. "Union are very compact, they are counting on hitting you on the break and it's not that they will be tired."
"They have undergone a great development, good continuity and they stick to their concept. When you are there where they are in the table at this stage of the season then it is fully deserved."